Mumford vanishing theorem explained

In algebraic geometry, the Mumford vanishing theorem proved by Mumford in 1967 states that if L is a semi-ample invertible sheaf with Iitaka dimension at least 2 on a complex projective manifold, then

H ^{i(X,L} ^{-1} ) =0 for i = 0 , 1 .

The Mumford vanishing theorem is related to the Ramanujam vanishing theorem, and is generalized by the Kawamata–Viehweg vanishing theorem.